{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# RT0-P0 Element for Poisson Equation in 2D"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This example is to show the rate of convergence of the linear finite element approximation of the Poisson equation on the unit square:\n",
    "\n",
    "$$- \\nabla (d \\nabla) u = f \\; \\hbox{in } (0,1)^2$$\n",
    "\n",
    "for the following boundary conditions\n",
    "- pure Dirichlet boundary condition: $u = g_D \\text{ on } \\partial \\Omega$.\n",
    "- Pure Neumann boundary condition: $d\\nabla u\\cdot n=g_N \\text{ on } \\partial \\Omega$.\n",
    "- mixed boundary condition: $u=g_D \\text{ on }\\Gamma_D, \\nabla u\\cdot n=g_N \\text{ on }\\Gamma_N.$\n",
    "\n",
    "Find $(\\sigma , u)$ in $H_{g_N,\\Gamma_N}(div,\\Omega)\\times L^2(\\Omega)$ s.t. \n",
    "\n",
    "$$ (d^{-1}\\sigma,\\tau) + (div \\tau, u)  = \\langle \\tau \\cdot n, g_D \\rangle_{\\Gamma_D} \\quad \\forall \\tau \\in H_{0,\\Gamma_N}(div,\\Omega)$$\n",
    "\n",
    "$$ (div \\sigma, v)                =  -(f,v) \\quad \\forall v \\in L^2(\\Omega) $$\n",
    " \n",
    " where \n",
    " \n",
    " $$H_{g,\\Gamma}(div,\\Omega) = \\{\\sigma \\in H(div,\\Omega); \\sigma \\cdot n = g  \\text{ on } \\Gamma \\subset \\partial\\Omega \\}.$$\n",
    "\n",
    " The unknown $\\sigma = d\\nabla u$ is approximated using the lowest order Raviart-Thomas element (RT0) and $u$ by piecewise constant element (P0).\n",
    "\n",
    "**References**\n",
    "\n",
    "\n",
    "**Subroutines**:\n",
    "\n",
    "    - PoissonRT0\n",
    "    - squarePoissonRT0\n",
    "    - mfemPoisson\n",
    "    - PoissonRT0mfemrate\n",
    "    \n",
    "The method is implemented in `PoissonRT0` subroutine and tested in `squarePoissonRT0`. Together with other elements (BDM1), `mfemPoisson` provides a concise interface to solve Poisson equation in mixed formulation. The RT0-P0 element is tested in `PoissonRT0mfemrate`. This doc is based on `PoissonRT0mfemrate`.    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## RT0 Lowest Order H(div) Element in 2D\n",
    "\n",
    "We explain degree of freedoms and basis functions for Raviart-Thomas element on a triangle. \n",
    "\n",
    "### Asecond orientation\n",
    "The dofs and basis depends on the orientation of the mesh. We shall use the asecond orientation, i.e., `elem(t,1)< elem(t,2)< elem(t,3)` not the positive orientation. Given an `elem`, the asecond orientation can be constructed by \n",
    "\n",
    "        [elem,bdFlag] = sortelem(elem,bdFlag);  % ascend ordering\n",
    "        \n",
    "Note that `bdFlag` should be sorted as well. \n",
    "\n",
    "The local edge is also asecond `[2 3; 1 3; 1 2]` so that the local orientation is consistent with the global one and thus no need to deal with the sign difference when the positive oritentation is used. Read [Simplicial complex in two dimensions](../mesh/scdoc.html) for more discussion of indexing, ordering and orientation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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1RE3+WtaAjszPX37o+hnX7N271+FwRGZCwLa4hmQdgRoF7keoK69XS6tjP03KVnInKdc4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\n/g+ot56I1Z+fMAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "node = [1,0; 1,1; 0,0];\n",
    "elem = [1 2 3];\n",
    "edge = [2 3; 1 3; 1 2];\n",
    "figure;\n",
    "subplot(1,2,1)\n",
    "showmesh(node,elem);\n",
    "findnode(node);\n",
    "findedge(node,edge,'all','rotvec');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Local bases of RT0 element\n",
    "\n",
    "Suppose `[i,j]` is the k-th edge. The two dimensional curl is a rotated graident defined as $\\nabla^{\\bot} f = (-\\partial_y f, \\partial _x f).$ The basis of this edge along with its divergence are given by\n",
    "\n",
    "$$ \\phi_k = \\lambda_i \\nabla^{\\bot} \\lambda_j - \\lambda_j \\nabla^{\\bot} \\lambda_i. $$\n",
    "\n",
    "Inside one triangular, the 3 bases corresponding to 3 local edges [2 3; 1\n",
    "3; 1 2] are:\n",
    "\n",
    "$$ \\phi_1 = \\lambda_2 \\nabla^{\\bot} \\lambda_3 - \\lambda_3 \\nabla^{\\bot} \\lambda_2. $$ \n",
    "\n",
    "$$ \\phi_2 = \\lambda_1 \\nabla^{\\bot} \\lambda_3 - \\lambda_3 \\nabla^{\\bot} \\lambda_1. $$\n",
    "\n",
    "$$ \\phi_3 = \\lambda_1 \\nabla^{\\bot} \\lambda_2 - \\lambda_2 \\nabla^{\\bot} \\lambda_1. $$\n",
    "\n",
    "The 3 dual bases are the line integral over orientated edges\n",
    "\n",
    "$$d_i(u) = \\int_{e_i} u \\cdot n_i \\, ds,$$\n",
    "\n",
    "where $n_i = t_i^{\\bot}$ is the rotation of the unit tangential vector of $e_i$ by $90^{\\deg}$ counterclockwise.\n",
    "\n",
    "It is straightforward to verify the \"orthogonality\":\n",
    "$$d_i(\\phi_j) = \\delta_{ij}.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Local to global index map\n",
    "\n",
    "Three local edges are `locEdge = [2 3; 1 3; 1 2]`. The pointer from the local to global index can be constructured by\n",
    "\n",
    "    [elem2dof,edge] = dofedge(elem);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "elem2dof =\n",
      "\n",
      "  8�3 uint32 matrix\n",
      "\n",
      "    8    3    2\n",
      "   11    6    5\n",
      "   15   10    9\n",
      "   16   13   12\n",
      "    5    3    1\n",
      "    7    6    4\n",
      "   12   10    8\n",
      "   14   13   11\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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trMEDIkpERHGoHJAJkn73vi9dPQM/z4fbUU2f5OyBIAAozNwDPx+di0+dnDf7I+sZAfAF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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "[node,elem] = squaremesh([0 1 0 1], 0.5);\n",
    "bdFlag = setboundary(node,elem,'Dirichlet');\n",
    "[elem,bdFlag] = sortelem(elem,bdFlag);\n",
    "showmesh(node,elem);\n",
    "findnode(node);\n",
    "findelem(node,elem);\n",
    "[elem2dof,edge] = dofedge(elem);\n",
    "findedge(node,edge,'all','rotvec');\n",
    "display(elem2dof);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Assembling the matrix equation\n",
    "\n",
    "We discuss several issues in the assembling.\n",
    "\n",
    "### Mass matrix\n",
    "\n",
    "The mass matrix can be computed by\n",
    "\n",
    "    M = getmassmatvec(elem2edge,area,Dlambda,'RT0');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### divergence matrix\n",
    "\n",
    "The ascend ordering orientation is not consistent with the induced orientation. The second edge would be `[3 1]` for the consistent orientation. So `[1 -1 1]` is used in the construction of div operator.\n",
    "\n",
    "For triangle t, the basis for the constant function space is $p = 1$, the characteristic function. So in the computation of divergence operator, `elemSign` should be used to correct the sign. In the output of `gradbasis`, `-Dlambda` is always the outwards normal direction. The signed area could be negative but in the ouput, `area` is the absolute value (for the easy of integration on elements) and `elemSign` is used to record elements with negative area."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  Columns 1 through 13\n",
      "\n",
      "     0     1    -1     0     0     0     0     1     0     0     0     0     0\n",
      "     0     0     0     0     1    -1     0     0     0     0     1     0     0\n",
      "     0     0     0     0     0     0     0     0     1    -1     0     0     0\n",
      "     0     0     0     0     0     0     0     0     0     0     0     1    -1\n",
      "    -1     0     1     0    -1     0     0     0     0     0     0     0     0\n",
      "     0     0     0    -1     0     1    -1     0     0     0     0     0     0\n",
      "     0     0     0     0     0     0     0    -1     0     1     0    -1     0\n",
      "     0     0     0     0     0     0     0     0     0     0    -1     0     1\n",
      "\n",
      "  Columns 14 through 16\n",
      "\n",
      "     0     0     0\n",
      "     0     0     0\n",
      "     0     1     0\n",
      "     0     0     1\n",
      "     0     0     0\n",
      "     0     0     0\n",
      "     0     0     0\n",
      "    -1     0     0\n",
      "\n"
     ]
    }
   ],
   "source": [
    "[Dlambda,area,elemSign] = gradbasis(node,elem);\n",
    "B = icdmat(double(elem2dof),elemSign*[1 -1 1]);\n",
    "display(full(B))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Boundary edges\n",
    "Direction of boundary edges may not be the outwards normal direction of the domain since now `elem` is ascend orientation. `edgeSign` is introduced to record this inconsistency.\n",
    "\n",
    "        edgeSign = ones(NE,1);\n",
    "        idx = (bdFlag(:,1) ~= 0) & (elemSign == -1); % first edge is on boundary\n",
    "        edgeSign(elem2edge(idx,1)) = -1;\n",
    "        idx = (bdFlag(:,2) ~= 0) & (elemSign == 1);  % second edge is on boundary\n",
    "        edgeSign(elem2edge(idx,2)) = -1;\n",
    "        idx = (bdFlag(:,3) ~= 0) & (elemSign == -1); % third edge is on boundary\n",
    "        edgeSign(elem2edge(idx,3)) = -1;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Examples\n",
    "\n",
    "### Mixed boundary condition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%% Setting\n",
    "[node,elem] = squaremesh([0,1,0,1],0.25); \n",
    "mesh = struct('node',node,'elem',elem);\n",
    "option.L0 = 1;\n",
    "option.maxIt = 4;\n",
    "option.printlevel = 1;\n",
    "option.elemType = 'RT0';\n",
    "pde = sincosNeumanndata;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Uzawa-type MultiGrid Preconditioned PCG \n",
      "#dof:      336,  #nnz:     1200, V-cycle:  1, iter: 16,   err = 6.10e-09,   time = 0.44 s\n",
      "Uzawa-type MultiGrid Preconditioned PCG \n",
      "#dof:     1312,  #nnz:     4832, V-cycle:  1, iter: 16,   err = 7.58e-09,   time =  0.1 s\n",
      "Uzawa-type MultiGrid Preconditioned PCG \n",
      "#dof:     5184,  #nnz:    19392, V-cycle:  1, iter: 16,   err = 9.33e-09,   time = 0.17 s\n",
      "Uzawa-type MultiGrid Preconditioned PCG \n",
      "#dof:    20608,  #nnz:    77696, V-cycle:  1, iter: 16,   err = 9.13e-09,   time = 0.51 s\n",
      "\n",
      " #Dof       h       ||u-u_h||    ||u_I-u_h||  ||sigma-sigma_h||||sigma-sigma_h||_{div}\n",
      "\n",
      "  336   1.25e-01   1.29904e-01   3.24734e-02   1.00431e+00   1.01710e+01\n",
      " 1312   6.25e-02   6.53343e-02   8.36322e-03   5.03316e-01   5.14701e+00\n",
      " 5184   3.12e-02   3.27108e-02   2.10609e-03   2.51787e-01   2.58126e+00\n",
      "20608   1.56e-02   1.63607e-02   5.27476e-04   1.25909e-01   1.29160e+00\n",
      "\n",
      " #Dof   Assemble     Solve      Error      Mesh    \n",
      "\n",
      "  336   1.20e-01   4.40e-01   1.20e-01   2.00e-02\n",
      " 1312   1.00e-01   1.00e-01   1.00e-01   1.00e-02\n",
      " 5184   1.00e-01   1.70e-01   6.00e-02   1.00e-02\n",
      "20608   7.00e-02   5.10e-01   1.20e-01   2.00e-02\n",
      "\n",
      "\n"
     ]
    },
    {
     "data": {
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De+9FuG+mzlKC4s+j+PNpzXlfVMSsxcaYJV1hSyDQ6vV6HQ5HYWGh1Wo9g67xUKte/we9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      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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GjRtRUVGUDnXp0iU5OZnaC8bkAVar1Xl5eVKplBrEzc1t7dq1zK/CXFdeeOEF3D59+nR6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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%% Mix Dirichlet and Neumann boundary condition.\n",
    "option.solver = 'uzawapcg';\n",
    "mesh.bdFlag = setboundary(node,elem,'Dirichlet','~(x==0)','Neumann','x==0');\n",
    "mfemPoisson(mesh,pde,option);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pure Neumann boundary condition\n",
    "\n",
    "In mixed formulation，the Neumann boundary condition for $d\\nabla u$ becomes the Dirichlet boundary condiiton for $\\sigma$. The space for $u$ is $L^2_0$ and thus one dof should be removed to have a non-singular system."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Uzawa-type MultiGrid Preconditioned PCG \n",
      "#dof:      336,  #nnz:     1102, V-cycle:  1, iter: 16,   err = 3.20e-09,   time = 0.15 s\n",
      "Uzawa-type MultiGrid Preconditioned PCG \n",
      "#dof:     1312,  #nnz:     4638, V-cycle:  1, iter: 17,   err = 3.67e-09,   time = 0.04 s\n",
      "Uzawa-type MultiGrid Preconditioned PCG \n",
      "#dof:     5184,  #nnz:    19006, V-cycle:  1, iter: 18,   err = 3.25e-09,   time = 0.19 s\n",
      "Uzawa-type MultiGrid Preconditioned PCG \n",
      "#dof:    20608,  #nnz:    76926, V-cycle:  1, iter: 18,   err = 8.29e-09,   time = 0.47 s\n",
      "\n",
      " #Dof       h       ||u-u_h||    ||u_I-u_h||  ||sigma-sigma_h||||sigma-sigma_h||_{div}\n",
      "\n",
      "  336   1.25e-01   1.35274e-01   4.88517e-02   1.00659e+00   1.01710e+01\n",
      " 1312   6.25e-02   6.55354e-02   1.00318e-02   5.03633e-01   5.14701e+00\n",
      " 5184   3.12e-02   3.27194e-02   2.33376e-03   2.51827e-01   2.58126e+00\n",
      "20608   1.56e-02   1.63613e-02   5.71884e-04   1.25914e-01   1.29160e+00\n",
      "\n",
      " #Dof   Assemble     Solve      Error      Mesh    \n",
      "\n",
      "  336   6.00e-02   1.50e-01   3.00e-02   0.00e+00\n",
      " 1312   1.00e-02   4.00e-02   2.00e-02   0.00e+00\n",
      " 5184   2.00e-02   1.90e-01   4.00e-02   0.00e+00\n",
      "20608   5.00e-02   4.70e-01   1.00e-01   1.00e-02\n",
      "\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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q/fbbbz/77DO8vWfPnqioKOJQQkLCkiVLiN2Ghoa6ujrZc9PT08m/73hGQVxc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\nxxKSPaZ4s8wAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "option.plotflag = 0;\n",
    "mesh.bdFlag = setboundary(node,elem,'Neumann');\n",
    "mfemPoisson(mesh,pde,option);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pure Dirichlet boundary condition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Uzawa-type MultiGrid Preconditioned PCG \n",
      "#dof:      336,  #nnz:     1232, V-cycle:  1, iter: 16,   err = 3.60e-09,   time = 0.09 s\n",
      "Uzawa-type MultiGrid Preconditioned PCG \n",
      "#dof:     1312,  #nnz:     4896, V-cycle:  1, iter: 16,   err = 6.53e-09,   time = 0.05 s\n",
      "Uzawa-type MultiGrid Preconditioned PCG \n",
      "#dof:     5184,  #nnz:    19520, V-cycle:  1, iter: 16,   err = 8.34e-09,   time = 0.16 s\n",
      "Uzawa-type MultiGrid Preconditioned PCG \n",
      "#dof:    20608,  #nnz:    77952, V-cycle:  1, iter: 16,   err = 8.49e-09,   time = 0.43 s\n",
      "\n",
      " #Dof       h       ||u-u_h||    ||u_I-u_h||  ||sigma-sigma_h||||sigma-sigma_h||_{div}\n",
      "\n",
      "  336   1.25e-01   1.29702e-01   3.08718e-02   1.00257e+00   1.01710e+01\n",
      " 1312   6.25e-02   6.53059e-02   7.92226e-03   5.03081e-01   5.14701e+00\n",
      " 5184   3.12e-02   3.27071e-02   1.99320e-03   2.51757e-01   2.58126e+00\n",
      "20608   1.56e-02   1.63602e-02   4.99086e-04   1.25905e-01   1.29160e+00\n",
      "\n",
      " #Dof   Assemble     Solve      Error      Mesh    \n",
      "\n",
      "  336   1.00e-02   9.00e-02   1.00e-02   0.00e+00\n",
      " 1312   0.00e+00   5.00e-02   1.00e-02   0.00e+00\n",
      " 5184   2.00e-02   1.60e-01   3.00e-02   1.00e-02\n",
      "20608   5.00e-02   4.30e-01   1.00e-01   1.00e-02\n",
      "\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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Z2pTjPTeFToA4380Z/+m+BYUBGQEMElfIyspKSEiQSqV0KiGBqwQABqAZHa5c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\nkyzPnj377LPPdu7cmZqaOnnyZHOLA9AC9B74k4qKCpz4CxM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      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%% Pure Dirichlet boundary condition.\n",
    "mesh.bdFlag = setboundary(node,elem,'Dirichlet');\n",
    "mfemPoisson(mesh,pde,option);"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "## Conclusion\n",
    "\n",
    "The optimal rates of convergence for $u$ and $\\sigma$ are observed, namely, 1st order for L2 norm of u, L2 norm of $\\sigma$ and H(div) norm of $\\sigma$. The 2nd order convergent rates between two discrete functions $\\|u_I - u_h\\|$ and $\\|\\sigma_I - \\sigma_h\\|$ are known as superconvergence.\n",
    "\n",
    "Triangular preconditioned GMRES (the default solver) and Uzawa preconditioned CG converges uniformly in all cases. Traingular preconditioner is two times faster than PCG although GMRES is used."
   ]
  }
 ],
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     "text": "MetaKernel Magics",
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